Forum — Daily Challenge
    • Categories
    • Recent
    • Tags
    • Popular
    • Users
    • Groups
    • Login

    How come when I put .3 repeated in a calculator times 3, it becomes 1, but on others it is .9?

    Day 1
    5
    10
    56
    Loading More Posts
    • Oldest to Newest
    • Newest to Oldest
    • Most Votes
    Reply
    • Reply as topic
    Log in to reply
    This topic has been deleted. Only users with topic management privileges can see it.
    • H
      hhh M0★ M1★ M2 M3★ M4★
      last edited by debbie

      How come when I put .3 repeated in a calculator times 3, it becomes 1, but on others it is .9?

      1 Reply Last reply Reply Quote 0
      • The Blade DancerT
        The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
        last edited by The Blade Dancer

        That's a matter of interpretation. Some matters of math are debated. For example, if you multiply 0.3 repeated 3 times, it's 0.9 repeated, which is soooooo close to 1, but not quite, hence other calculators counting it as 0.9 (sort of an abbreviation in math terms, they wouldn't go on with the 9's forever). However, if you convert 0.3 repeated into fraction form, it is 1/3, and 3 x 1/3 is 1. It all depends on how you look at it.

        Hope this helped.

        The Blade Dancer
        League of Legends, Valorant: Harlem Charades (#NA1)
        Discord: Change nickname if gay#7585

        1 Reply Last reply Reply Quote 0
        • Potato2017P
          Potato2017 M5★
          last edited by

          Actually, most people agree that 0.9999999999999999... is 1.
          Here's a way you can look at this. If two numbers are different, you should be able to find a number between them. Can you find a number between 0.999999999999999999... and 1? If not, then they can't be different numbers.
          Another way:

          $$\begin{aligned} 1/3&=0.333333333333333... \\ \text{Multiply bo}&\text{th sides by 3}\\ 1&=0.999999999999999... \end{aligned} $$

          One final way:

          $$\begin{aligned} \text{Let }x&=0.9999999999999999...\\ \text{Then }10x&=9.9999999999999999...\\ \text{Subtract the }&\text{first equation from the first.}\\ 9x&=9\\ x&=1\\ \end{aligned} $$

          The best Potato
          aops: Potato2017
          yt: http://bit.ly/potatosubscribe
          discord: Potato2017#1822 (it's tent#0001 now)
          tetr.io: https://ch.tetr.io/u/potato2017
          -Potato2017

          1 Reply Last reply Reply Quote 1
          • N
            nastya MOD M0 M1 M2 M3 M4 M5
            last edited by debbie

            Hi @userusername,
            @The-Darkin-Blade and @Potato2017 are both correct and provided great mathematical proofs of this fact. Thank you all! 🙂

            Thinking about it, it is true that some calculators are "cleverer" than others, and they "know" that \(\overline{0.333...}\times 3=1.\) It could be for different reasons: some calculators have this fact stored as basic initial information for other calculations, while other calculators can transform some of the repeating digits of the fractions, so when they receive \(\overline{0.333...}\times 3\) they think of it as \(^1/_3\times 3,\) and that's why we get \(1\) as an answer. The other, less "clever", calculators just multiply these numbers and we get \(\overline{0.333...}\times 3=\overline{0.999...}\) as a result. Or, maybe, they are more sophisticated than we think, and they want to clearly show what the actual answer is. 😉

            But, in the end, for us, the answer \(\overline{0.999...}\) and \(1\) are the same. The easiest way to realize this and put it in your head as not like something that you just "know", but something that you "understand", is to realize that the number \(\overline{0.999...}\) has infinitely many \(9's,\) so it is infinitely close to \(1,\) and there is no actual difference between \(\overline{0.999...}\) and \(1.\) At least, I think of it in this way 🙂

            Hope this helped you to find your own understanding of what is going on!

            1 Reply Last reply Reply Quote 0
            • WalnutW
              Walnut M0 M1 M2
              last edited by

              so 1/3 is 0.3 repeating, right? 1/3 *3 is 1, but 0.3 repeating *3 is 0.9 repeating. So, we know that 0.9 repeating is 1.

              Walnut He

              1 Reply Last reply Reply Quote 1
              • The Blade DancerT
                The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
                last edited by

                All a matter of interpretation

                The Blade Dancer
                League of Legends, Valorant: Harlem Charades (#NA1)
                Discord: Change nickname if gay#7585

                1 Reply Last reply Reply Quote 1
                • Potato2017P
                  Potato2017 M5★
                  last edited by Potato2017

                  If you put \(1/3 \cdot 3 \)into almost any calculator, 0.99999999 will come out. This is because when it calculated 1/3, it rounded 0.3333333333333333333... into 0.333333333333. When it calculated 0.3333333333333*3, it forgot that 0.33333333333333 was rounded. Good calculators will give you 1.

                  Edit: the asterisks made it italicized 😛 i fixed it

                  The best Potato
                  aops: Potato2017
                  yt: http://bit.ly/potatosubscribe
                  discord: Potato2017#1822 (it's tent#0001 now)
                  tetr.io: https://ch.tetr.io/u/potato2017
                  -Potato2017

                  1 Reply Last reply Reply Quote 1
                  • The Blade DancerT
                    The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
                    last edited by

                    Personally I like to think of 0.99 repeating as a real small tad less than 1.

                    The Blade Dancer
                    League of Legends, Valorant: Harlem Charades (#NA1)
                    Discord: Change nickname if gay#7585

                    1 Reply Last reply Reply Quote 1
                    • H
                      hhh M0★ M1★ M2 M3★ M4★
                      last edited by

                      Oh, and why when I do .3 times 2 it is 0.66666667 instead of 0.66666666?

                      N 1 Reply Last reply Reply Quote 0
                      • N
                        nastya MOD M0 M1 M2 M3 M4 M5 @hhh
                        last edited by

                        Hi @userusername,
                        It is because your calculator rounds the number \(\overline{0.66666666...}\) to the number \(0.66666667.\)
                        The same thing happens when you want to round the number \(\overline{0.316495...}\) to its hundredths. Instead of \(0.31\) you will get \(0.32,\) since the next digit after \(1\) is \(6\) that is \(\geq 5,\) so the rounding goes up.

                        1 Reply Last reply Reply Quote 0

                        • 1 / 1
                        • First post
                          Last post
                        Daily Challenge | Terms | COPPA